Generalized Von Neumann Universe and Non-Well-Founded Sets
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913059971268608 |
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| author | Zhang, Eugene |
| author_facet | Zhang, Eugene |
| contents | In this paper, a generalized version of the von Neumann universe known as the total universe is proposed to formally introduce non-well-founded sets that include infinitons, semi-infinitons and quasi-infinitons in Russell's paradox. All three infinitons are part of infinitely generated sets that are generators of non-well-founded sets. Combining the well-founded sets with the non-well-founded sets, the total universe is a model of ZF minus the axiom of regularity and free of Russell's paradox. The axiom of regularity can not define the well-founded sets and is invalid in any system consistent with ZF set theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00581 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generalized Von Neumann Universe and Non-Well-Founded Sets Zhang, Eugene Logic 03C55, 03C75, 03E99 In this paper, a generalized version of the von Neumann universe known as the total universe is proposed to formally introduce non-well-founded sets that include infinitons, semi-infinitons and quasi-infinitons in Russell's paradox. All three infinitons are part of infinitely generated sets that are generators of non-well-founded sets. Combining the well-founded sets with the non-well-founded sets, the total universe is a model of ZF minus the axiom of regularity and free of Russell's paradox. The axiom of regularity can not define the well-founded sets and is invalid in any system consistent with ZF set theory. |
| title | Generalized Von Neumann Universe and Non-Well-Founded Sets |
| topic | Logic 03C55, 03C75, 03E99 |
| url | https://arxiv.org/abs/2304.00581 |